Natalie Sexton jokes that her earliest memory is being rocked to sleep on the machinery bottling her mother’s line of all-natural juices. She was just an infant when Marygrace Sexton started Natalie’s Orchid Island Juice Company in 1990, naming it after her.

“This is all I’ve known,” Ms. Sexton said.

Twenty-six years later, she is preparing to take over her family’s business in the coming decade. The company, based in Fort Pierce, Fla., has expanded from its humble beginnings. Her mother had to borrow the butcher’s truck at night to make deliveries. Now, the company has 100 employees and distribution in 32 states and 34 countries.